1. Field of the Invention
The present invention relates generally to a quantizer, and more particularly, relates to a noise shaping quantizer.
2. Description of the Prior Art
The quantizer is a major component of any digital signal processing system. Quantization error unavoidably occurs during quantization by the quantizer. Various methods have therefore been used to reduce quantization error, at least in the frequency range of signals of necessary. One method of reducing quantization error is called noise shaping.
FIG. 1 is a block diagram of a multi stage noise shaping quantizer 101 having multiple stages of loops as taught in Patent Reference 1 (Japanese Patent Gazette No. 8-2024-B2). Adders 111 and 113, a first local quantizer 115, a limiter 117, a subtractor 119, and a delay element 121 render a main loop 103 in this multi stage noise shaping quantizer 101. The main loop 103 functions as a single integration noise shaping quantizer implementing first-order noise shaping. Another adder 123, a second local quantizer 125, a subtractor 127, and a feedback circuit 129 render a sub-loop 105. The sub-loop 105 functions as a multi-integration noise shaping quantizer implementing first, second, or higher order noise shaping.
Another delay element 131 and a subtractor 133 render a differentiator 107. The differentiator 107 differentiates the output of the sub-loop 105 corresponding to the noise shaping order of the main loop 103. The output of the main loop 103 and the output of the sub-loop 105 differentiated by the differentiator 107 are added by an adder 109 and outputted. Thus, a multi stage noise shaping quantizer is implemented of which noise shaping order is equal to “the noise shaping order of the sub-loop 105 plus 1.” The transfer function H(z) of the feedback circuit 129 in this example provides the sub-loop 105 with a second-order or higher noise shaping characteristic. The output of the feedback circuit 129 in the sub-loop 105 is inputted to the adder 113 of the main loop 103. As a result, the output of the feedback circuit 129 is added to the input to the first local quantizer 115 (that is, the output of the adder 111). The multi stage noise shaping quantizer 101 thus can suppress the quantization error inputted to the sub-loop 105 by adding or subtracting a specific value to or from the input to the first local quantizer 115 based on the output of the feedback circuit 129, and thus enables the sub-loop 105 to operate normally. The first local quantizer 115 then performs quantizing operation to the input, which is equal to the output of the adder 111 plus the output of the feedback circuit 129, and outputs the resultant to the limiter 117. The limiter 117 checks the condition of the differentiator 107, and limits the value of the signal outputted from the limiter 117 based on the condition of the differentiator 107.
The magnitude of the quantization error occurred in the main loop 103 is less than or equal to the range of values of signals inputted to the first local quantizer 115 at the clock (clock cycle) when the limiter 117 does not operate. At the clock when the limiter 117 operates, however, the magnitude of the quantization error occurred in the main loop 103 is greater than the quantization error inferred to occur at the clock when the limiter 117 does not operate. Therefore, the value of the signal inputted to the first local quantizer 115 by way of the delay element 121 and the adder 111 at the clocks after the limiter 117 operates increases, and as a consequence, the first local quantizer 115 may overflow.
FIG. 2 describes the relationship between the value range which may be inputted to the first local quantizer 115 and the actual signal examples actually inputted to the first local quantizer 115. How the first local quantizer 115 in the multi stage noise shaping quantizer 101 in FIG. 1 overflows is described with reference to FIG. 2. The input range 151 of values that can be inputted to the first local quantizer 115 includes the input signal portion 163 such as an audio signal, quantization error portion 161, the feedback output portion 159 from the sub-loop 105, and a signal margin portion 157. The signal margin portion 157 is provided to allow for limit error in the operation of the limiter 117. On the other hand, the input signal 165 to the first local quantizer 115 includes the input signal portion 163, the quantization error portion 161, the feedback output portion 159 of the sub-loop 105, and the limit error portion 155. As a result, the actual input signal 165 to the first local quantizer 115 may exceed the input range 151 of the first local quantizer 115, and an overflow portion 153 may result. This overflow portion 153 is also fed back after one clock. The overflow portion 153 that is fed back is then gradually eliminated over a number of clocks.
The likelihood of an overflow occurring can obviously be suppressed by increasing the size of the margin 157. However, the other portions 159, 161, and 163 must be decreased as the signal margin portion 157 is increased. This narrows the bandwidth that can be used for the input signal portion 163. As a result, the dynamic range of the first local quantizer 115 is also reduced.
Patent Reference 1: Japanese patent gazette No. 8-2024-B2
Non-Patent Reference 1: “A 17-bit oversampling D-to-A conversion technology using multistage noise shaping”, Matsuya, Yasuyuki et al., IEEE Journal of Solid State Circuit, Vol. 24, No. 4, August, 1989, pp. 969-975